Origin of the term sine

It is well-known that "sine" comes from the Latin word "sinus", meaning a "fold", or a pocket.

However, its reference to the length of the half-chord on the unit circle remains still rather obscure.

I recently came over an explanation that makes perfect sense, and here it is:
1. In Sanskrit, the term "jiva" means half-chord.
2. Arab mathematicians made use both of Greek and Hindu sources; in particular, they retained the term "jiva" from Sanskrit.
3. In Arab writing, one ignores vowels, so that in Arabic texts, the technical term "jiva" is written in the same manner as the common word "jaib" that means..."fold/pocket"
4. Thus, when Arab works were transcribed into Latin, the transcriber naturally thought he should insert "sinus" where "jiva" was standing.

And thus, the trigonometric function gained its strange name..

I found this explanation in Asgeir Aaboe's "Episodes from the early history of Mathematics" (1964).
Aaboe (1922-2007) was professor in the history of sciences at Yale, until his retirement in 1992.
He died this January, here's an obituary:
http://www.yale.edu/opa/v35.n16/story14.html [Broken]